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Developments In Business Simulation & Experiential Exercises, Volume 22, 1995
AN ANALYTICAL ADVERTISING MODEL APPROACH TO THE DETERMINATION OF MARKET DEMAND
Kenneth R. Goosen, University of Arkansas at Little Rock
ABSTRACT
most business enterprise simulations. Cannon (1984)
contended that the teaching of advertising should be based
on more theory:
The dynamic nature of decision-making in business
enterprise simulations depends on the computation of
aggregate market demand. The aggregate demand models in
simulations are essentially based on the economic model of
an oligopoly industry. Despite the mathematical rigor in
which the models of market demand are incorporated in
business simulations, these models in many aspects are gross
over simplifications of the real world. The major weakness
of the aggregate market demand model in business
enterprise simulations is the simplistic treatment of the
advertising decision. This paper presents a proposed demand
model, which places primary importance on marketing
concepts.
Nevertheless, with the maturation of advertising as a
discipline, many of us have begun to search for a less
descriptive, more theory-oriented approach. We would like
our courses to teach students how to make the decision that
older texts simply describe-- how to formulate advertising
strategy, how to make media selection, how to set
advertising budgets, and so forth.
The implication of Cannon’s comments regarding
simulations is somewhat obvious. Advertising in business
simulations should be based on current marketing theory
rather than the early economic models of demand
INTRODUCTION
NEED FOR AN IMPROVED ADVERTISING MODEL
Advertising in microeconomic models is treated as a
parameter that causes a shift in the demand curve.
Consequently, this same limited viewpoint generally prevails
in business enterprise simulations. The inadequate modeling
of the advertising variable diminishes the perception of
simulation realism. This lack of a realistic advertising model
in simulations has been noted several times in simulation
literature. In a paper in which he argued for
noncompensatory demand functions Lambert (1979) stated:
The need for an improved model of advertising as one
determinant of market demand is evident when it is realized
that current simulations still adhere to the simplistic
economic treatment of advertising.
The aim of advertising is both to shift to the right the
demand curve faced by the individual seller and to make it
less elastic . . .The purpose of advertising is not simply to
attract a greater buying public for a product, but to attract
consumers away from the competition. (Albrecht, Jr., 1974)
While the lack of a comprehensive theory of the behavior of
sales in response to marketing tactics is a handicap, still
every effort must be made in designing these simulations to
insure that sales behavior at least appears plausible.
The economic view that advertising is no more than an
assigned value to a single parameter in a demand equation
undermines the real importance and complexity of
advertising in the decision-making process.
More recently, Carvalho (1993) pointed out the inadequate
treatment of advertising in simulations:
Examples of the standard treatment of advertising in
aggregate demand models can be found in two articles by
Gold and Pray (1982, 1984). They defined aggregate
demand as:
Q = g1 P- (g2+g3)PM+(g4-g5)MR+(g6 g7)R. In this equation,
advertising or M (marketing expenditures) is simply a
parameter in the total equation. The model requires no more
than finding the sum of the advertising budgets of the
different firms in the industry. Important advertising
variables and parameters are
Market demand functions do not model individuals’
purchase decision processes; they model a condition or state
of affairs in the market. A market demand function indicates
the quantity that will be purchased at each price by all
people in the market. The process by which an individual
buyer arrives at the decision to buy or not buy a particular
product is not modeled by the market demand function.
Advertising is a far more complex variable than treated in
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Developments In Business Simulation & Experiential Exercises, Volume 22, 1995
The purpose of advertising is to make potential buyers
respond favorably to the firm’s offering. It seeks to do this
by providing information to customers, by trying to modify
their desires, and by supplying reasons to prefer the
particular company’s products.
excluded from this aggregate demand model. Furthermore,
another basic problem with the aggregate demand model, as
traditionally used in business simulations, is that when
advertising is increased it is not clear whether the increase in
market demand is the result of more potential customers in
the market or because a higher percentage of the same
potential customers have purchased. In the first instance,
more salesmen to make calls would be required; and in the
second instance, an increase in the sales-calls ratio is
implied. Also, it is not clear whether all customers in the
market are buying, and if so, whether some customers are
purchasing more units than others. The concept of buyers
and nonbuyers in the market is not recognized in aggregate
demand models currently being used.
The definition provides several important clues about to how
to develop a more analytical and realistic model of
advertising. The definition makes clear that advertising
informs customers. Without advertising customers are
uninformed and, therefore, are unable to purchase.
Consequently, two important concepts are implied: informed
customers and uninformed customers. Uninformed
customers, of course, are nonbuying customers. Also, from
real world experience we know that even some informed
customers do not always purchase. Consequently, two other
useful concepts emerge from the definition of the purpose of
advertising: buying customers and nonbuying customers.
The assumptions underlying the advertising decision in the
aggregate demand model do not allow the simulation
designer to provide any meaningful information that can be
used by the decision maker to make a thoughtful and
analytical advertising decision. For example, in most
simulations no definition of the potential market size is
given. Consequently, the decision for budgeted advertising is
at best a guess. In order to simulate reality, the decisionmaker should be given some market demographics that
makes possible meaningful analysis.
The decision-maker in making the advertising budget
decision at a minimum would probably ask the following
questions:
How many potential customers are in the market?
What dollar amount of advertising is required to reach one
potential customer?
What effect does repetition of the same message have on
response to the advertising?
What will be the response of customers to the amount
budgeted advertising?
The primary objective here is too develop a model that
provides the firm (student decision-maker) with a rational
basis for determining how much to advertise. Specifically,
the objective is to answer the questions: (1) what are the
elements and variables that must be considered in
determining the size of the advertising budget, and (2) what
is the nature of a model that incorporates these variables?
The analytical advertising model being presented does
directly address these questions.
BASIC THEORY OF AN ANALYTICAL
ADVERTISING DEMAND MODEL
THE NATURE OF ADVERTISING
Advertising is recognized to be a strategic management
decision involving different levels of complexity.
Consequently, the model being presented does not pretend to
encompass all aspects of advertising. The total advertising
decision involves other factors such as the advertising
message, the selection of media, timing of advertising, and
methods of evaluating results. This paper is not concerned
with these elements and is limited to the development of a
model that realistically deals with the advertising budget
decision. An excellent definition of advertising that provides
the basis for an improved theory has been provided by
Cotler (1967):
From experience we know that some customers may be
more informed than others. A customer who has seen an ad
several times may be more informed that one who has seen
an ad only once. Repeated exposure increases the desire to
buy. Therefore, the need to measure the degree of being
informed results from the concept of an advertising exposure
index.
When the concepts of informed customers and uninformed
customers and buying customers and nonbuying customers
are recognized, a functional relationship may be established
between the exposure index and the candidates for a sale
percentages. This relationship may be called the
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Developments In Business Simulation & Experiential Exercises, Volume 22, 1995
candidate for sale of more than one firm will eventually
select only one industry firm from which to purchase in a
given period. The selection of the specific firm is affected by
both the number of ad exposures and the advertised price.
The number of customers that actually purchase can also be
a factor of the number of salesmen, credit terms, and quality
of products.
proportion of response function. This functional relationship
then provides a foundation for a more realistic and analytical
model to the determination of market demand. This function
is illustrated in Figure 2.
When it is recognized that the market consists of buying and
nonbuying customers, it is then axiomatic that the
percentage of customers purchasing in a given period will be
less than 100%. The percentage of the potential market that
respond to advertising may be called candidates for a sale.
Some potential customers in a market require more than one
unit of advertising to be a candidate for a sale.
Consequently, the repeat exposure of the same advertising
will prove beneficial. The repeat exposure of an ad is a
determinant of market demand. Potential customers are more
likely to purchase as the exposure to advertising increases.
Based upon the above analysis, the development of an
analytical advertising model at a minimum would include
the following concepts:
1.
2.
3.
4.
5.
6.
7.
An essential element of the analytical model of demand is a
functional relationship between the exposure index and the
percentage of potential customers responding to advertising.
Potential customers (maximum market size)
Informed customers
Uninformed customers
Buying customers
Nonbuying customers
Advertising cost per customer
Exposure index
Proportion of response function
Industry candidates for a sales
Proportion of purchase function
Firm candidates for a sale
Advertising Cost per Customer
Advertising can be treated as if it consists of discreet units.
For example, one flyer or one brochure is a discreet unit.
Even TV and radio advertising can be considered to consist
of discreet units. If 5,000 out of 50,000 potential customers
are viewers of TV at a specific time slot, then a one-time ad
may be considered as consisting of 5,000 units of
advertising. A discreet unit of advertising can be assigned a
specific cost per unit.
The analytical advertising demand model being proposed is
summarized as in Figure 1.
Potential Customers
Given the number of potential customers, the advertising
cost per unit, and the desired exposure rate, the preparation
of the advertising budget becomes a relatively easy task. If
the advertising cost per potential customer is known, then
the total advertising required to inform all potential
customers would be:
The market for a product consists of an identifiable segment
or class of individuals who can benefit from the use of the
product. These individuals may be labeled potential
customers. Some potential customers readily perceive a
benefit and require very little advertising. Others potential
customers have no or very little knowledge of the product
but are capable of benefiting or being influenced by
advertising.
Some potential customers will never purchase the product
regardless of the amount of advertising. Consequently, the
response to advertising will always be less than 100%.
Separately identifying or isolating these different types of
potential customers is difficult if not impossible. Therefore,
the all customers of the market must be the target of
advertising.
The amount of advertising required to expose the total
potential market to an ad can be easily calculated. However,
the unknown factor is the number of exposures necessary to
cause a desired percentage of the market to respond.
Therefore, the number of times to repeat an ad becomes an
important decision.
A potential customer can be a candidate for a sale of more
than one firm in the industry. A potential customer who is a
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Developments In Business Simulation & Experiential Exercises, Volume 22, 1995
Importance of the Industry Demand Curve
Computing Industry and Firm Exposures Indices
In the model being proposed, the industry demand curve
applies only to informed customers who have made a
conscious decision to seriously consider purchasing in the
current period. Since the number of informed customers can
vary significantly with the amount of advertising, the
demand curve must be presented on a relative (percentage)
basis. Rather than showing units at each price, the demand
curve must be restructured to show the percentage of the
informed customers that will purchase at a given price. The
relationship of price to the percentage purchasing may be
called a proportion of purchase distribution function.
Because the proposed advertising demand model depends on
the extent to which customers have been informed, the
calculation of both firm and industry exposure indices are
required. The calculated exposure index identifies the
appropriate firm and industry candidates for sale
percentages.
In Figure 3, a traditional demand curve converted to a
proportion of purchase distribution is illustrated. The details
and mechanics of constructing this distribution is explained
in a later section.
There is no need in the proposed model for both an industry
demand curve and an individual firm demand curves as
required in the traditional aggregate demand models. What is
being allocated is not units sold but rather informed
customers willing to buy (candidates for a sale ) from a
specific firm. Allocation is accomplished by using firm
candidates for a sale rather than units of product. This model
requires calculation of candidates for a sale from both the
firm and industry viewpoints.
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Developments In Business Simulation & Experiential Exercises, Volume 22, 1995
then can be used to compute the total number of industry
candidates for a sale:
Proportion of Purchase Function
The industry TCFS (equation 3) has been computed without
regard to price. Unless all firms have set the lowest possible
price, not all candidates will purchase. Therefore, the TCFS
must be adjusted for the industry price. The industry price
which is an average of firm prices may be calculated:
Given the IP, then the appropriate proportion of purchase
percentage can be determined and used to compute the
industry price adjusted candidates for a sale.
The industry exposure index is the average number of times
that individuals in the market have been the recipient of ads
from all firms. The total includes all repeat exposures of the
same ad.
Proportion of Response Function
The appropriate proportion of purchase percentage is found
by reference to a proportion of purchase function such as the
one illustrated in Figure 3. For example, at a price of $30,
the proportion of purchase percentage would be 50%. The
PACFS will be allocated to each firm according to each
firm’s share of the total of all price adjusted candidates for a
sale.
As previously mentioned, a functional relationship exists
between the industry El and the percentage of potential
customers who become candidates for a sale. The percentage
of the candidates for a sale in response to advertising is a
type of effectiveness index. This relationship is illustrated in
Figure 2. The functional relationship between the exposure
index and the percentage of customers responding can be
easily programmed by using Goosen’s and Kusel’s (1993)interpolation method.
Industry Candidates for a Sale
A customer who has been informed by one or more units of
advertising and who has been favorably impressed may be
defined as a candidate for a sale in the current period. The
total number of industry candidates for a sale in a given time
period is a direct function of the total firm advertising and
advertised price.
Computation of Firm Candidates for a Sale
Computations of the candidates for a sale of each firm
involves:
1.
2.
The exposure index, as explained above, can be used to
identify the candidate for a sale percentage. This percentage
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Computing the Exposure Index (El) of each firm
Computing the total candidates for a sale before
price)
Developments In Business Simulation & Experiential Exercises, Volume 22, 1995
Explanation of Price Weights
3. Computing the price adjusted candidates for a sale
4. Allocating the industry price adjusted candidates
for a sale according to the ratios of the firms’
price adjusted candidates for a sale.
The firms’ El’s may be defined as:
To understand the purpose of weights based on price, it is
necessary to consider certain attributes of a demand curve.
At each price, a specific number of units may be sold.
Assuming that each customer purchases only 1 unit, the
number of units at each price also represent the percentage
of the total market (potential customers) that is purchasing.
Consequently, the industry demand curve can be stated as a
proportion of purchase distribution independent of quantity.
Assume the following:
Given the El of each firm, the candidates for a sale
percentage can be determined by reference to the same
functional relationship used in computing the industry TCFS
(See Figure 2).
Since it has been assumed that the response to advertising
and the willingness to purchase is affected by advertised
price, the candidates for a sale of each firm require
adjustment for a price weight. The lower the price, the
higher the weight.
Assuming price will never be lower than $10, the maximum
sales (customers) will be 40. At each price the corresponding
units can be stated as a percentage of maximum aggregate
demand. At a price of $30 only 50% of the potential market
will purchase. At a price of $30, the proportion of purchase
percentage was computed by dividing quantity at the price of
$30 by the quantity at a price of $10. The quantity at the
price of $40 represents the maximum market demand.
The allocation percentage of each firm then may be
computed as:
At each price of a given demand curve, the related units can
be stated as a percentage of the total market demand. The
advantage of using percentages rather than quantity in the
demand curve is that a limit to the number of units that may
be purchased can be easily specified. Also a shift in demand
can be accomplished by simply changing the value of
maximum market demand which also happens to be the
quantity value at the lowest allowed price.
The proportion of purchase distribution derived from the
demand curve permits the elimination of those informed
potential customers who are not willing to pay the advertised
price. The remaining customers are willing to pay the price.
However, because these remaining potential candidates for a
sale of firm A may also be willing to buy from Firm B, then
an allocation of the industry candidates for a sale must be
made according to the price adjusted candidates for a sales
percentages of the individual firms.
Given the set of allocation percentages, each firm’s share of
the industry candidates for a sale can be allocated as follows:
Now that each firm has been assigned its share of the total
industry candidates for a sale, other factors, if desired, such
as credit and number of salesmen can be brought into play to
determine the actual units of product sold by the firm.
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Developments In Business Simulation & Experiential Exercises, Volume 22, 1995
62.5%. Therefore, the industry price adjusted candidates for
sale would be 5,156. The allocation of the industry PACFS
is illustrated in figure 4.
Illustration of Analytical Advertising Model
The proposed model can be easily illustrated. Assume the
following data:
CONCLUSIONS AND SUMMARY
TPC = 10,000
ACPU = 2.00
Based on the above assumed data and decisions, the
following computations may be made.
The advantage of the proposed analytical advertising model
is that it explicitly recognizes several important advertising
variables. Price has little or no relevance unless a customer
knows of the product and knows of the existence of a
specific firm. An informed customer is a necessary
prerequisite for a sale.
The analytical advertising model approach:
(1)
(2)
(3)
(4)
(5)
emphasizes the number of potential customers in a
market.
emphasizes the number of individuals responding to
an ad.
emphasizes the effectiveness of advertising in
generating a response.
emphasizes the competition of firms for the same pool
of candidates for a sale.
allows for each firm to manage other factors in
converting candidates for a sale into customers that
actually purchase.
Potential customers who have received one or more
exposures of an ad become a candidate for a sale if they
react favorably to the ad’s message. As the exposure index
increases, the number of candidates for a sale increases. A
potential customers may become a candidate for a sale of
one than one firm
Candidates for a sale of each firm then evaluate the firm
based on advertised price. Some customers will cease to
become a candidate for a sale at this point because the
advertised price is too high. However, not all customers
reject a firm because it has a higher price. The percentage of
customers that continue to be a candidate for a sale after
evaluation of price is determined by the appropriate
proportion of purchase percentage.
At an exposure index of 3, the candidate for sales percentage
is 82.5%. Given a total market potential of 10,000, the
industry candidates before price adjustment for sale would
be 8,250. The proportion of purchase percentage at an
average price of $25 is
The distribution of potential informed customers that make
up each firm’s candidates for sale is the same as the
distribution of customers as determined by the industry
demand curve. Consequently, only a market demand curve
presented as a proportion of purchase distribution is
required.
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Developments In Business Simulation & Experiential Exercises, Volume 22, 1995
REFERENCES
The traditional model allocates aggregate demand in terms
of units of product. The proposed advertising model
allocates industry candidates for a sale based on the firm’s
individual candidates for a sale. Total demand in units then
is simply each firm’s total candidates for a sale multiplied by
the average number of units that each customer is assumed
to purchase.
Albrecht, Jr., W.P. (1974) Imperfect
Economics, Prentice-Hall, Inc., 531
competition,
Carvalho, G. (1993) A dynamic market share allocation
model for computerized business simulations, Developments
in Business Simulations & Experiential Exercises, 20, 31.
The analytical advertising model for determining aggregate
demand has now been presented. A comparison of elements
and factors with the traditional aggregate demand is helpful
in visualizing differences and similarities:
Gold, S., & Pray T.F. (1984) Simulating market- and firm
level demand functions in computerized business
simulations. Simulations & Games, 15, 346-363
Gold S. & T. F. Pray (1984) Modeling non-price factors in
the demand functions of computerized business simulations,
Developments in Business Simulation & Experiential
Exercises.
Goosen, K. R. & J. Kusel (1993) An interpolation approach
to developing mathematical functions for business
simulations. Simulation & Gaming, 24. 76-90.
Cotler, P. (1967) “Advertising Decisions”, Marketing
Management, Prentice Hall, P.456
Cannon, Hugh M. (1987). From Theory to Practice: A model
for teaching beginning advertising, Developments in
Business Simulation & Experiential Exercises, 1 4, 34
Lambert, D.R. (1979) On compensatory demand functions in
marketing simulations, Experiential learning Enters the
Eighties, Brenenstuhl and Biggs, Editors, (Tempe, Arizona):
The Bureau of Business and Economic Research, Arizona
State University, 80
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